Sequential logic synthesis expands the solution space compared to combinational logic synthesis by reasoning about the reachable states of memory elements, leading to better Power-Performance-Area (PPA) outcomes. As gate costs continue to rise in advanced technologies, sequential logic synthesis is gaining significant traction within the EDA community as a powerful alternative. This paper introduces a scalable algorithm for don’t-care-based sequential logic synthesis, leveraging sequential k-step induction to perform redundancy removal and resubstitution under Sequential Observability Don’t Cares (SODCs). SODCs generalize Observability Don’t Cares (ODCs) by explicitly considering reachable states, making SODC-based optimization a challenging problem due to dependencies and alignment issues between the base case and inductive case in k-step induction. Our approach overcomes these challenges, fully utilizing the potential of SODCs without limiting the solution space. We rigorously prove the correctness of our approach, discuss some limitations arising from bounded-step induction, and analyze how our approach can effectively be used in practice to exploit obscure optimization opportunities. Implemented as part of an industrial tool, our algorithm achieves an average -6.9% area improvement after technology mapping compared to state-of-the-art sequential synthesis methods, and further provides 3.16% and 1.06% reductions in combinational and sequential areas, respectively, in post place-and-route results. Furthermore, all optimizations are efficiently verified using industrial sequential verification tools.

Superconducting electronics provide us with cryogenic digital circuits that can rival established technologies in performance and energy consumption. Today, the lack of tools for the design of large-scale integrated superconducting circuits is a major obstacle to their deployment. Few research institutions and companies have contributed to making such tools available. This review focuses on methods, algorithms, and open-source design tools for logic synthesis of superconducting circuits in two major families: single-flux quantum (SFQ) circuits and adiabatic quantum flux parametron (AQFP).

Sequential logic synthesis can provide better Power-Performance-Area (PPA) than combinational logic synthesis since it explores a larger solution space. As the gate cost in advanced technologies keeps rising, sequential logic synthesis provides a powerful alternative that is gaining momentum in the EDA community. In this work, we present a new scalable algorithm for don't-care-based sequential logic synthesis. Our new approach is based on sequential k-step induction and can apply both redundancy removal and resubstitution transformations under Sequential Observability Don't Cares (SODCs). Using SODC-based optimizations with induction is a challenging problem due to dependencies and alignment of don't cares among the base case and the inductive case. We propose a new approach utilizing the full power of SODCs without limiting the solution space. Our algorithm is implemented as part of an industrial tool and achieves a 6.9% average area improvement after technology mapping when compared to state-of-the-art sequential synthesis methods. Moreover, all the new sequential optimizations can be verified using state-of-the-art sequential verification tools.

In logic circuits, the number of fanouts a gate can drive is limited, and such limits are tighter in emerging technologies such as superconducting electronic circuits. Moreover, some such technologies, e.g., adiabatic quantum-flux-parametron (AQFP), pose additional constraints such as the need for balanced input-to-output paths to ensure proper signal propagation. In this work, targeting emerging technologies, we study the problem of re-synthesizing a logic network with bounded-fanout gates while minimizing area for a given depth. Namely, we 1) formulate the fanout-bounded synthesis (FBS) problem for a fixed target logic depth as an integer linear program (ILP), 2) propose a scalable top-down approach to construct a feasible solution to the ILP, and 3) extend both the exact and the heuristic approaches to the setting of path-balanced networks. Using our ILP, we obtain the global optimum solutions for a number of benchmarks that serve as ground truth for evaluating heuristic algorithms in both general and path-balanced FBS. Our heuristic algorithm for general FBS achieves an 11.82% better area than the state of the art with matching or better delays while attaining the optimum/near-optimum area for several considered benchmarks. For the path-balanced setting, our heuristic approach achieves 8.76% better delay on average with an average area improvement of 0.5% when using AQFP as the exemplar technology, while achieving more than 17% better delays on several benchmarks.

In logic circuits, the number of fanouts a gate can drive is limited, and such limits are tighter in emerging technologies such as superconducting electronic circuits. In this work, we study the problem of resynthesizing a logic network with bounded-fanout gates while minimizing area. We 1) formulate this problem for a fixed target logic depth as an integer linear program (ILP) and present exact solutions for small logic networks, and 2) propose a top-down approach to construct a feasible solution to the ILP which yields an efficient algorithm for fanout bounded synthesis. When using the minimum depth achievable with unbounded fanouts as the target logic depth, our top-down approach achieves 11.82% better area as compared to the state-of-the-art with matching or better delays.

Adiabatic superconducting devices are promising candidates to develop high-speed/low-power electronics. Advances in physical technology must be matched with a systematic development of comprehensive design and simulation tools to bring superconducting electronics to a commercially viable state. Being the technology fundamentally different from CMOS, new challenges are posed to design automation tools: library cells are controlled by multi-phase clocks, they implement the majority logic function, and they have limited fanout. We present a product-level RTL-to-GDSII flow for the design of Adiabatic Quantum-Flux-Parametron (AQFP) electronic circuits, with a focus on the special techniques used to comply with these challenges. In addition, we demonstrate new optimization opportunities for graph matching, resynthesis, and buffer/splitter insertion, improving the state-of-the-art.

Most logic synthesis algorithms work on graph representations of logic functions with nodes associated with arbitrary logic expressions or simple logic functions and iteratively optimize such graphs. While recent multilevel logic synthesis efforts focused primarily on graphs with 2-input nodes such as AND and OR gates, the recently proposed paradigm of Majority-Inverter Graphs (MIGs) instead uses the 3-input Majority gate as the node function. As this technique proved to be a success, it is natural to ask: are there other 3-input gates better suited for logic synthesis? Motivated by this question, we investigate the relative advantages of 3-input gates as constituents of logic networks. We consider representative gates from each of the ten nondegenerate 3-input NPN classes and study how powerful they are at representing Boolean functions. Using SAT-based exact synthesis, we evaluate each 3-input gate using the minimum number of such gates (together with inverters) needed to synthesize all 4-input Boolean functions and a subset of frequent 5-input and 6-input Boolean functions. We show that the logic gate Dot(x,y,z) \mathrel \mathrel \mathop:= x ⊕(z Vxy) outperforms the rest in terms of expressive power. We further confirm this observation by showing that Dot-Inverter Graph representations are more than 14% smaller as compared to MIG representations of EPFL benchmarks.